Basic properties
| Modulus: | \(3328\) | |
| Conductor: | \(3328\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(192\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3328.dv
\(\chi_{3328}(43,\cdot)\) \(\chi_{3328}(75,\cdot)\) \(\chi_{3328}(147,\cdot)\) \(\chi_{3328}(179,\cdot)\) \(\chi_{3328}(251,\cdot)\) \(\chi_{3328}(283,\cdot)\) \(\chi_{3328}(355,\cdot)\) \(\chi_{3328}(387,\cdot)\) \(\chi_{3328}(459,\cdot)\) \(\chi_{3328}(491,\cdot)\) \(\chi_{3328}(563,\cdot)\) \(\chi_{3328}(595,\cdot)\) \(\chi_{3328}(667,\cdot)\) \(\chi_{3328}(699,\cdot)\) \(\chi_{3328}(771,\cdot)\) \(\chi_{3328}(803,\cdot)\) \(\chi_{3328}(875,\cdot)\) \(\chi_{3328}(907,\cdot)\) \(\chi_{3328}(979,\cdot)\) \(\chi_{3328}(1011,\cdot)\) \(\chi_{3328}(1083,\cdot)\) \(\chi_{3328}(1115,\cdot)\) \(\chi_{3328}(1187,\cdot)\) \(\chi_{3328}(1219,\cdot)\) \(\chi_{3328}(1291,\cdot)\) \(\chi_{3328}(1323,\cdot)\) \(\chi_{3328}(1395,\cdot)\) \(\chi_{3328}(1427,\cdot)\) \(\chi_{3328}(1499,\cdot)\) \(\chi_{3328}(1531,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{192})$ |
| Fixed field: | Number field defined by a degree 192 polynomial (not computed) |
Values on generators
\((1535,261,769)\) → \((-1,e\left(\frac{61}{64}\right),e\left(\frac{1}{6}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 3328 }(43, a) \) | \(-1\) | \(1\) | \(e\left(\frac{101}{192}\right)\) | \(e\left(\frac{29}{64}\right)\) | \(e\left(\frac{83}{96}\right)\) | \(e\left(\frac{5}{96}\right)\) | \(e\left(\frac{131}{192}\right)\) | \(e\left(\frac{47}{48}\right)\) | \(e\left(\frac{1}{48}\right)\) | \(e\left(\frac{49}{192}\right)\) | \(e\left(\frac{25}{64}\right)\) | \(e\left(\frac{49}{96}\right)\) |